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8. Sequences and Series
hard
જો $1 + r + r^2 + …. + r^n = (1 + r) (1 + r^2) (1 + r^4) (1 + r^8),$ હોય તો $n$ નું મૂલ્ય કેટલું થાય ?
A
$13$
B
$14$
C
$15$
D
$16$
Solution
$1 + r + r^2 + …… + r^n = (1 + r) (1 + r^2) + (1 + r^4) (1 + r^8)$ છે.
$ \Rightarrow \,\,\frac{{1\,\, – \,\,{r^{n\, + \,1}}}}{{1\,\, – \,\,r}}= (1 + r) (1 + r^2) (1 + r^4) (1 + r^8)$
$⇒ (1 – r^{n + 1}) = (1 – r) (1 + r) (1 + r^2) (1 + r^4) (1 + r^8)$
$ (1 -r^{ n + 1})= (1 – r^{16})$
$⇒ n + 1 = 16 ⇒ n = 15$
Standard 11
Mathematics
